so what advantage does testing at 50 yds have other than actually getting on paper?
Solving a problem is a process of elimination for me anyway....
So what do we have? A shooter, a rifle. scope mounts, a scope and ammunition.
Using a box of factory loaded ammunition eliminates the possible human error factor of self loaded ammunition. Using a chronograph will further confirm the consistency off the ammunition, especially if it is self loaded.
No point in continuing to shoot at 100 yards and achieving 10 inch groups.
Get an experienced buddy to help with the shooting @ 25 and then 50 yards.
1. Shooter-could well be a shooter error. Not everybody can handle the recoil of certain rifles/calibers, this is reality no matter how dearly such a person would want to own and shoot a bigger bore rifle. Many folks have issues with 375 H&H recoil. A .416 Rigby has more recoil and recoil velocity than the 375 H&H. 37.3 and 16.3 for the 375 H&H from a 9 pound rifle and 58.1 and 19.3 for the Rigby from a 10 pound rifle(404 is 41 and 16.1 which is why it has a reputation for being low in recoil when compared). Flinching will have you shooting all over the place. So getting 2.5" groups @ 25 and 5 inch groups @ 50 yards from 2 different shooters will show you that there is something wrong with either the rifle or the shooters, therefore you can look there to solve the problem. Not saying that the OP cannot handle the recoil but then eliminate that and move on.
2. Rifle-again if the shooters are both confident and competent with the recoil and their shooting ability, above groupings at 25 and 50 yards will again point to an issue with the rifle. I doubt that it is a bad barrel.
3. Scope mounts-removing the scope and mounts will eliminate this possibility.
4. Scope-see point 3.
5. Ammunition-yes unlikely that this is the issue. However for this simple test use factory ammo over a chrony and eliminate any ammo issues. Bigger bore rifles although not tack drivers should not be shooting that bad. They are also less prone, when compared to smaller high velocity cartridges to show bad accuracy due to some small issue with action screws etc. The screws need to be tight yes but tight is tight and should not have such a large effect on a 416 Rigby. Wrong powder(burn rate and load density), wrong primers(poor ignition in huge cartridges) etc. can all have a effect. Yes agreed 10 inches would be an exception. However combining for example low load density and poor ignition rate could mean 4 MOA ammo and add to that some flinching and you easily stretch that to 10 inches.
So use a box of 20 Factory ammo and two competent shooters and start with the basics and work up from there, that is what I would do anyway.
Good luck and hope you get it sorted.